The site's operator Hafren Dyfrdwy said the decision to close the public facilities followed the Welsh Government's move to put the country into Tier 4 over concerns about the spread of Covid-19.
Visitor Site Experience Lead Dominic Robinson said: “This is absolutely the right decision as we try to help limit the spread of coronavirus.
"We know how popular the site is but the wellbeing and safety of our visitors, communities and colleagues is the most important thing at this time.
"The car parks will be closed and so we’re asking people not to travel to the site.”
The closures will be in place for the foreseeable future at the dam.
“We’d encourage everyone to follow government guidelines and we hope everyone understands and supports our decision,” Mr Robinson added.
A Facebook post stated: "With Wales now in Tier 4 restrictions our car parks and toilets will be closed until the restrictions ease.
"Please stay safe and follow the Governments’ guidance on staying local for exercise. Wishing you all the best Christmas and we are looking forward to welcoming you all back sometime soon."